Coarse infinite-dimensionality of hyperspaces of finite subsets

We consider infinite-dimensional properties in coarse geometry for hyperspaces consisting of finite subsets of metric spaces with the Hausdorff metric. We see that several infinite-dimensional properties are preserved by taking the hyperspace of subsets with at most n points. On the other hand, we prove that, if a metric space contains a sequence of long intervals coarsely, then its hyperspace of finite subsets is not coarsely embeddable into any uniformly convex Banach space. As a corollary, the hyperspace of finite subsets of the real line is not coarsely embeddable into any uniformly convex Banach space. It is also shown that every (not necessarily bounded geometry) metric space with straight finite decomposition complexity has metric sparsification property.

Convergence results of a faster iterative scheme including multi-valued mappings in Banach spaces

In this paper, we study M-iterative scheme in the new context of multi-valued generalized ?-nonexpansive mappings. A uniformly convex Banach space is used as underlying setting for our approach. We also provide a new example of generalized ?-nonexpasive mappings. We connect M iterative scheme and other well known schemes with this example, to show the numerical efficiency of our results. Our results improve and extend many existing results in the current literature.

Approximating Fixed Points of Operators Satisfying (RCSC) Condition in Banach Spaces

Let K be a nonempty subset of a Banach space E. A mapping T:K→K is said to satisfy (RCSC) condition if each a,b∈K, 1/2a−Fa≤a−b⇒Fa−Fb≤1/3a−b+a−Fb+b−Fa. In this paper, we study, under some appropriate conditions, weak and strong convergence for this class of maps through M iterates in uniformly convex Banach space. We also present a new example of mappings with condition (RCSC). We connect M iteration and other well-known processes with this example to show the numerical efficiency of our results. The presented results improve and extend the corresponding results of the literature.

Browder’s Convergence Theorem for Multivalued Mappings in Banach Spaces without the Endpoint Condition

We prove Browder’s convergence theorem for multivalued mappings in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm by using the notion of diametrically regular mappings. Our results are significant improvement on results of Jung (2007) and Panyanak and Suantai (2020).

Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization

The class of Suzuki mappings is reanalyzed in connection with a three-steps Thakur procedure. The setting is provided by a uniformly convex Banach space, that is normed space endowed with some symmetric geometric properties and some topological properties. Once more, the fact that property ( C ) holds on as a generalized nonexpansiveness condition is emphasized throughout some examples. One example uses the setting of R 2 with the Taxicab norm. It is further included in a numerical experiment in connection with seven iteration procedures, resulting a visual analysis of convergence.

A Study on p-Cyclic Orbital Geraghty type Contractions

Consider a metric space and the non empty sub sets, of X. A map called p-cyclic orbital Geraghty type of contraction is introduced. Convergence of a unique fixed point and a best proximity point for this map is obtained in a uniformly convex Banach space setting. Also, this best proximity point is the unique periodic point of such a map.

Vector-valued Littlewood-Paley-Stein Theory for Semigroups II

Inspired by a recent work of Hytönen and Naor, we solve a problem left open in our previous work joint with Martínez and Torrea on the vector-valued Littlewood-Paley-Stein theory for symmetric diffusion semigroups. We prove a similar result in the discrete case, namely, for any $T$ which is the square of a symmetric diffusion Markovian operator on a measure space $(\Omega , \mu )$. Moreover, we show that $T\otimes{ \textrm{Id}}_X$ extends to an analytic contraction on $L_p(\Omega ; X)$ for any $1<p<\infty $ and any uniformly convex Banach space $X$.

Common Fixed Points for Weak and Strong Convergence Results

<div><p> <em>In this paper, we study the approximation of common fixed points for more general classes of mappings through weak and strong convergence results of an iterative scheme in a uniformly convex Banach space. Our results extend and improve some known recent results.</em></p></div>